Abstract

We analyze the unidimensional (UD) continuous-variable quantum key distribution protocol in a finite size scenario under realistic conditions. The dependence of the secret key rate on realistic parameters is analyzed numerically. A method of calculating the optimal ratio to divide the data samples in order to achieve the largest secret key rate is proposed. When the data samples are large, the superiority of the UD protocol in data processing becomes apparent. It is expected that the features and methods presented in this paper will aid in the exploration of the latent capacity of the UD protocol as well as the development of further applications.

© 2017 Optical Society of America

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2017 (4)

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

A. Leverrier, “Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction,” Phys. Rev. Lett. 118(20), 200501 (2017).
[PubMed]

Z. Qu and I. B. Djordjevic, “High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing,” Opt. Express 25(7), 7919–7928 (2017).
[PubMed]

2016 (4)

D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
[PubMed]

T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
[PubMed]

2015 (5)

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent States,” Phys. Rev. Lett. 114(7), 070501 (2015).
[PubMed]

2014 (1)

L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

2013 (2)

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

2012 (5)

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

2010 (1)

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

2009 (6)

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102(11), 110504 (2009).
[PubMed]

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[PubMed]

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[PubMed]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Q. Dinh Xuan, Z. Zhang, and P. L. Voss, “A 24 km fiber-based discretely signaled continuous variable quantum key distribution system,” Opt. Express 17(26), 24244–24249 (2009).
[PubMed]

2007 (2)

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

2006 (3)

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[PubMed]

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[PubMed]

2005 (1)

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

2004 (1)

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

2003 (1)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

2002 (2)

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
[PubMed]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[PubMed]

2001 (1)

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).

1999 (1)

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).

Acín, A.

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[PubMed]

Alléaume, R.

Andersen, U. L.

T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

Assad, S. M.

O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

Bai, Z. L.

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Berta, M.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Bloch, M.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Bobrek, M.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Bowen, W. P.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

Braunstein, S. L.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

Brouri, R.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

Cerf, N. J.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[PubMed]

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[PubMed]

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).

Cirac, J. I.

R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102(11), 110504 (2009).
[PubMed]

Debuisschert, T.

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Diamanti, E.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Dinh Xuan, Q.

Djordjevic, I. B.

Du, P. Y.

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Duhme, J.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
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Dušek, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Filip, R.

L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

Fossier, S.

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
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S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Franz, T.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
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F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
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Furrer, F.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
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F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
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García-Patrón, R.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
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J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
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Gehring, T.

T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

Grangier, P.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
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A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[PubMed]

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
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Grice, W.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Grosshans, F.

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
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F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
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Händchen, V.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
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Huang, D.

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
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D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
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Huang, L. L.

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

Huang, P.

D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
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D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
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Jacobsen, C. S.

T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

Jouguet, P.

Karpov, E.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Kunz-Jacques, S.

Lam, P. K.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
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C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
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Lance, A. M.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
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Lassen, M.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
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Leuchs, G.

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
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Leverrier, A.

A. Leverrier, “Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction,” Phys. Rev. Lett. 118(20), 200501 (2017).
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A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent States,” Phys. Rev. Lett. 114(7), 070501 (2015).
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P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
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A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
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Levy, M.

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).

Li, H.

Li, Y. M.

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Lin, D.

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
[PubMed]

Liu, W. Y.

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

Lloyd, S.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

Lo, H. K.

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

Lodewyck, J.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Lougovski, P.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Lütkenhaus, N.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
[PubMed]

Madsen, L. S.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

McLaughlin, S. W.

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Navascués, M.

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[PubMed]

Ottaviani, C.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

Pache, P.

Pacher, C.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

Painchault, P.

Peev, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Peng, K. C.

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Pirandola, S.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

Pooser, R.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Qi, B.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

Qian, L.

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

Qu, Z.

Ralph, T. C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
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T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).

Renner, R.

R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102(11), 110504 (2009).
[PubMed]

Ruppert, L.

L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

Scarani, V.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

Schnabel, R.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

Scholz, V. B.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Shapiro, J. H.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

Sharma, V.

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

Silberhorn, Ch.

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
[PubMed]

Spedalieri, G.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

Symul, T.

O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

Thearle, O.

O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

Tomamichel, M.

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Tualle-Brouri, R.

P. Jouguet, S. Kunz-Jacques, T. Debuisschert, S. Fossier, E. Diamanti, R. Alléaume, R. Tualle-Brouri, P. Grangier, A. Leverrier, P. Pache, and P. Painchault, “Field test of classical symmetric encryption with continuous variables quantum key distribution,” Opt. Express 20(13), 14030–14041 (2012).
[PubMed]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

Usenko, V. C.

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).

L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

Van Assche, G.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).

Villing, A.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

Voss, P. L.

Wang, P.

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

Wang, S. F.

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

Wang, T.

Wang, X. Y.

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Weedbrook, C.

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

Wenger, J.

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

Werner, R. F.

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Yang, S. S.

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

Zeng, G.

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
[PubMed]

D. Huang, P. Huang, H. Li, T. Wang, Y. Zhou, and G. Zeng, “Field demonstration of a continuous-variable quantum key distribution network,” Opt. Lett. 41(15), 3511–3514 (2016).
[PubMed]

Zhang, Z.

Zhou, Y.

Chin. Phys. B (1)

Y. M. Li, X. Y. Wang, Z. L. Bai, W. Y. Liu, S. S. Yang, and K. C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26, 040303 (2017).

Chin. Phys. Lett. (2)

X. Y. Wang, Z. L. Bai, S. F. Wang, Y. M. Li, and K. C. Peng, “Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise,” Chin. Phys. Lett. 30(1), 010305 (2013).

X. Y. Wang, Z. L. Bai, P. Y. Du, Y. M. Li, and K. C. Peng, “Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication,” Chin. Phys. Lett. 29(12), 124202 (2012).

Nat. Commun. (2)

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).
[PubMed]

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3, 1083 (2012).
[PubMed]

Nat. Photonics (2)

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

Nature (1)

F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[PubMed]

New J. Phys. (1)

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11(4), 045023 (2009).

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (10)

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).

X. Y. Wang, W. Y. Liu, P. Wang, and Y. M. Li, “Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 95(6), 062330 (2017).

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).

N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).

J. Lodewyck, M. Bloch, R. García-Patrón, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A 76(4), 042305 (2007).

B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A 76(5), 052323 (2007).

L. Ruppert, V. C. Usenko, and R. Filip, “Long-distance continuous-variable quantum key distribution with efficient channel estimation,” Phys. Rev. A 90(6), 062310 (2014).

O. Thearle, S. M. Assad, and T. Symul, “Estimation of output-channel noise for continuous-variable quantum key distribution,” Phys. Rev. A 93(4), 042343 (2016).

Phys. Rev. Lett. (12)

A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent States,” Phys. Rev. Lett. 114(7), 070501 (2015).
[PubMed]

A. Leverrier, “Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction,” Phys. Rev. Lett. 118(20), 200501 (2017).
[PubMed]

R. Renner and J. I. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102(11), 110504 (2009).
[PubMed]

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[PubMed]

A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. 102(18), 180504 (2009).
[PubMed]

R. García-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97(19), 190503 (2006).
[PubMed]

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97(19), 190502 (2006).
[PubMed]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109(10), 100502 (2012).
[PubMed]

Ch. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89(16), 167901 (2002).
[PubMed]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[PubMed]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[PubMed]

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
[PubMed]

Phys. Rev. X (1)

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “Locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).

Quantum Inf. Comput. (1)

T. Gehring, C. S. Jacobsen, and U. L. Andersen, “Single-quadrature continuous-variable quantum key distribution,” Quantum Inf. Comput. 16(13), 1081–1095 (2016).

Rev. Mod. Phys. (2)

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).

Sci. Rep. (1)

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6, 19201 (2016).
[PubMed]

Other (2)

P. Papanastasiou, C. Ottaviani, and S. Pirandola, “Finite size analysis of measurement device independent quantum cryptography with continuous variables,” https://arxiv.org/abs/1707.04599 .

C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “CV MDI QKD: Composable Security against Coherent Attacks,” https://arxiv.org/abs/1704.07924 .

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Figures (9)

Fig. 1
Fig. 1 PM and EB schemes of the UD protocol under realistic conditions.
Fig. 2
Fig. 2 Regions of the UD protocol under realistic and ideal conditions.
Fig. 3
Fig. 3 Three-dimensional plots for the secret key rates in the secure region from different visual angles.
Fig. 4
Fig. 4 Minimum secret key rate K m versus V y B 1 for different reconciliation efficiencies under realistic conditions.
Fig. 5
Fig. 5 (a) Secret key rate K m versus the phase quadrature variance V y B 1 at different detection efficiencies. (b) The secret key rate K m versus the detection efficiency η.
Fig. 6
Fig. 6 (a) Secret key rate K m as a function of the phase quadrature variance V y B 1 with different electronic noise values. (b) The secret key rate K m versus the electronic noise υ e .
Fig. 7
Fig. 7 Secret key rate versus distance in the SY and UD coherent state protocols for different excess noise values.
Fig. 8
Fig. 8 Secret key rate versus the proportions of m/N and l/N.
Fig. 9
Fig. 9 Secret key rates versus the proportions m/N and l/Nfor different total samples.

Tables (1)

Tables Icon

Table 1 Optimal proportions and secret key rates versus total number of samples.

Equations (27)

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γ AS =[ V 0 V( V 2 1 ) 0 0 V 0 ( V 2 1 )/V V( V 2 1 ) 0 V 2 0 0 ( V 2 1 )/V 0 1 ].
γ A B 1 =[ 1+ V M 0 T x V M ( 1+ V M ) 1/4 0 0 1+ V M 0 C y B 1 T x V M ( 1+ V M ) 1/4 0 T x ( V M +1+ χ linex ) 0 0 C y B 1 0 V y B 1 ],
γ AB =[ 1+ V M 0 η T x V M ( 1+ V M ) 1/4 0 0 1+ V M 0 C y B η T x V M ( 1+ V M ) 1/4 0 η T x ( V M +1+ χ totx ) 0 0 C y B 0 V y B ],
V y B =η( V y B 1 + χ hom ) and  C y B = C y B 1 η .
K =β I AB χ BE ,
I AB = 1 2 log 2 ( 1+ V M 1+ χ totx ).
χ BE =S( ρ E )S( ρ E x B ),
χ BE =S( ρ A B 1 )S( ρ ARH x B ).
λ 1,2 2 = 1 2 ( A± A 2 4B ),
A=1+ V y B 1 + V M + V y B 1 ( ε x + V M ) T x +2 C y B 1 ( 1+ V M ) 1 4 V M T x ,
B=( V y B 1 ( 1+ V M ) ( C y B 1 ) 2 1+ V M )( 1+ ε x T x ).
λ 3,4 2 = 1 2 [ C± C 2 4D ],   λ 5 =1
C= A(1+ υ e )+(( ε x T x +1)( V M +2)+ V M T x A)η 1+ ε x T x η+ V M T x η+ υ e ,
D= B(1+ υ e η)+(1+ V M )(1+ ε x T x )η 1+ ε x T x η+ V M T x η+ υ e .
χ BE =G( λ 1 )+G( λ 2 )-G( λ 3 )-G( λ 4 ) ,
γ A B 1 +iΩ0 ,
( C y B 1 C 0 ) 2 V M (1+ V M ) χ linex 1+ χ linex ( V y B 1 V 0 ) ,
K m f = n N (β I AB χ BE δ PE Δ(n)) ,
Δ(n)7 log 2 (2/ ϵ ¯ ) n ,  n 10 4 ,
x B = t x x A + z x ,
χ BE V y B 1 | t, σ 2 >0 .
t ^ x = i=1 m x A i x B i i=1 m x A i 2   and   σ ^ x 2 = 1 m2 i=1 m ( x B i t ^ x x A i ) 2
t ^ x ( t x , σ x 2 i=1 m x Ai 2 )and (m2) σ ^ x 2 σ x 2 χ 2 (m2)
V ^ y B = 1 l1 i=1 l ( y Bi y ¯ B ) 2 ,
(l1) V ^ y B V y B ~ χ 2 (l1) .
CI( t x )=[ t ^ x Δ t ^ x , t ^ x +Δ t ^ x ], CI( σ x 2 )=[ σ ^ x 2 Δ σ ^ x 2 , σ ^ x 2 +Δ σ ^ x 2 ], CI( V ^ y B )=[ V ^ y B Δ V ^ y B , V ^ y B +Δ V ^ y B ],
T x min 1 η ( η T ^ x z δ PE /2 1+η T ^ x ε ^ x + υ e m V M ) 2 , ε x max ε ^ x + z δ PE /2 ( 1+η T ^ x ε ^ x + υ e ) 2 η T ^ x m , V ymax B 1 V ^ y B 1 + z δ PE /2 ( η( V ^ y B 1 1 )+1+ υ e ) 2 η l .

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